Vertical Line Test

Front

What is the Vertical Line Test?

Back

A method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

If a graph passes the Vertical Line Test, what can we conclude?

Back

The graph represents a function.

Front

If a graph does not pass the Vertical Line Test, what can we conclude?

Back

The graph does not represent a function.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x, there is one unique y.

Front

What is an example of a relation that is not a function?

Back

The equation x^2 + y^2 = 1 is not a function because a vertical line can intersect it at two points.

Front

What is the definition of a function?

Back

A relation where each input (x) has exactly one output (y).

Front

What is a non-function?

Back

A relation where at least one input (x) has more than one output (y).

Front

How can you visually identify a function from a graph?

Back

By using the Vertical Line Test; if a vertical line crosses the graph more than once, it is not a function.

Front

What is the significance of the Vertical Line Test in mathematics?

Back

It helps to quickly determine if a graph represents a function without needing to analyze the equation.